Assume that the weights (Ibs) of paper discarded each week by households are normally distributed with a mean of 9.43lb and a standard deviation of 4.17lb (These estimates are taken from the "Garbage Project" at the University of Arizona.) Let X = amount of paper discarded by a single home What is the distribution of X? If 12 homes are selected at random and monitored for their paper disposal, what is the sampling distribution of xbar? Under the scenario of question #2, what is the probability that the mean paper discarded is between 10 and 12 lb?Suppose instead that 30 homes are chosen. What now is the probability that the mean is between 10 and 12 lb? If 100 homes are chosen? Suppose that upon examining 100 homes in the Ames, IA area, you find that the mean amount of discarded paper is 10.5. What would you say about the claim made by the U of Arizona as "the true state" of all US housedholds